A cylindrical steel rod of length $0.10 \mathrm{~m}$ and thermal conductivity $50 \mathrm{~W} \cdot \mathrm{m}^{-1} \mathrm{~K}^{-1}$ is welded end to end to copper rod of thermal conductivity $400 \mathrm{~W} \cdot \mathrm{m}^{-1} . \mathrm{K}^{-1}$ and of the same area of cross section but $0.20 \mathrm{~m}$ long. The free end of the steel rod is maintained at $100^{\circ} \mathrm{C}$ and that of the copper and at $0^{\circ} \mathrm{C}$. Assuming that the rods are perfectly insulated from the surrounding, the temperature at the junction of the two rods-

• Correct answer
  A

  $20^{\circ} \mathrm{C}$
• B

  $30^{\circ} \mathrm{C}$
• C

  $40^{\circ} \mathrm{C}$
• D

  $50^{\circ} \mathrm{C}$

Solution

$\frac{50 \times \mathrm{A} \times(100-\mathrm{T})}{0.1}=\frac{400 \times \mathrm{A} \times(\mathrm{T}-0)}{0.2}$

Hence, the correct answer is option: 'A'.